Theoretical backgound for bileptonic gauge bosons is reviewed, both the
SU(15) GUT model and the 3-3-1 model. Mass limits on bileptons are discussed
coming from $e^+e^-$ scattering, polarized muon decay and muonium-antimuonium
conversion. Discovery in $e^-e^-$ at a linear collider at low energy (100GeV)
and high luminosity ($10^{33}/cm^2/s$) is emphasised.}Comment: 9 pages LaTeX. Talk at Third International Workshop on
  Electron-Electron Interactions at TeV Energies, UC-Santa Cruz. December
  10-12, 199

Frampton, Paul H.

English

arXiv

Theoretical backgound for bileptonic gauge bosons is reviewed, both the SU(15) GUT model and the 3-3-1 model. Mass limits on bileptons are discussed coming from e+e− scattering, polarized muon decay and muonium-antimuonium conversion. Discovery in e−e− at a linear collider at low energy (100GeV) and high luminosity (1033/cm2/s) is emphasised

Carolina Digital Repository

arXiv:hep-ph/0002017v1  1 Feb 2000BILEPTON RESONANCE IN ELECTRON-ELECTRON SCATTERINGPAUL H. FRAMPTONDepartment of Physics and Astronomy,University of North Carolina, Chapel Hill, NC 27599-3255E-mail: frampton@physics.unc.eduABSTRACTTheoretical backgound for bileptonic gauge bosons is reviewed, both the SU(15)GUT model and the 3-3-1 model. Mass limits on bileptons are discussed comingfrom e+e− scattering, polarized muon decay and muonium-antimuonium con-version. Discovery in e−e− at a linear collider at low energy (100GeV) and highluminosity (1033/cm2/s) is emphasised.Introduction.It is a stunning historical fact that e−e− collisions have never been studied at acenter of mass energy above 1.12 GeV as published in 1971 by Richter et al1. Therewere plans to explore e−e− at DESY but these were abandoned when money ran out.The three large projects in HEP for the US (and internationally) for the foreseeablefuture are: NLC, MC and VLHC. Of these the NLC is for the first decade of thetwenty-first century; the other two are for the second decade. The NLC is presentlya multi- billion dollar project primarily aimed at e+e−.A topic of this workshop is: should it have also e−e− capability?Why has e−e− been so neglected? Firstly e+e− is where Z′can be found - oftencited as the most conservative extension of the Standard Model (SM). By contraste−e− is an exotic, empty channel because it has double electric charge and leptonnumber L = 2. Surely, e−e− would allow only checks of higher-order quantum elec-trodynamics. But physics is an experimental science!e−e− Resonance.Such a resonance must have L = 2 and Q = 2. It must be a boson. For spinzero a doubly-charged Higgs scalar, the coupling is a free parameter and is genericallysmall. For a spin one gauge boson, the coupling is large and prescribed. Bileptongauge bosons give a pronounced peak at s = M2. But, as our main emphasis here,the resonance tail is detectable at much lower energy.Bilepton gauge bosons were first suggested in the context of SU(15) grand unification2.First recall that in SU(5) grand unification with families each in 5+ 1̄0 the reasonfor B violation is that the second rank tensor 1̄0 has indefinite B and L quantumnumbers.If SU(5) had fermions only in the 5 then B and L would necessarily be conservedperturbatively.The presence of the 1̄0 is what causes the indeterminacy of B and L and allowsmediation of proton decay in the gauge sector.Since proton decay remains elusive the idea in SU(15) is to prohibit it in thegauge sector. The 15 helicity states in each family are assigned to a 15 of SU(15).Whereupon each gauge boson has definite B and L according to which pair of thefundamental fermions it couples.The first family is assigned to:15 = (uRL , uGL , uBL , dRL , dGL , dBL ; ūRL , ūGL , ūBL , d̄RL , d̄GL , d̄BL ; e+L , νeL, e−L)and similarly for the second and third families.It is clear that all of the 224 gauge bosons of SU(15) have definite B and L.Anomaly cancellation is by mirror fermions - disfavored aesthetically but notphenomenologically.The pattern of spontaneous symmetry breaking is:SU(15)MG−→ SU(12)q × SU(3)lMB−→ SU(6)L × SU(6)R × U(1)B × SU(3)lMA−→ SU(3)C × SU(2)L × U(1)YIn the breaking at MA color SU(3)C is embedded in SU(6)L×SU(6)R as (3+3, 1)+(1, 3̄ + 3̄).SU(2)L is embedded in SU(6)L × SU(3)l with 6L = 3(2)L and 3L = 2L + 1LU(1)Y is contained in SU(6)R × U(1)B × SU(3)l according to:Y =√3Λ +√23B +√3Ywith Λ, B and Y generators of SU(6)R, U(1)B and SU(3)l, respectively, normalizedas SU(15) matrices withTr(ΛaΛb) = 2δab.Explicitly, these normalized SU(15) generators areΛ =1√3diag(000000,−1− 1− 1111, 000)B =√32diag(131313131313,−13− 13− 13− 13− 13− 13, 000)and Y = 1√3diag(000000, 000000, 2− 1− 1)RENORMALIZATION GROUPµdαi(µ)/dµ = Biα2i (µ)with matching conditions, at MA:α−13C(MA) =12α−16L (MA) +12α−16R(MA)α−12L (MA) =34α−16L (MA) +14α−13l (MA)α−11Y (MA) =920α−16R(MA) +110α−1B (MA) +920α−13l (MA)at MB:α6L(MB) = α6R(MB) = αB(MB) = α12q(MB)and at MG:α12q(MG) = α3l(MG) = α15(MG)The results can be tabulated, as shown in this Table of typical values for the threebreaking scales of SU(15)MA(GeV ) MB(GeV ) MG(GeV )250 4.0× 106 6.0× 106500 5.8× 106 8.9× 106103 8.3× 106 1.3× 1072× 103 1.2× 107 1.9× 107There is one input parameter, say MA.MB and MG are outputs.At low energies (MA) the gauge bosons under SU(6)L × SU(6)R × U(1)B × SU(3)lare, with respect to the standard model:35L = (8, 3)0 + (8, 1)0 + (1, 3)035R = 2(8, 1)0 + (8, 1)±1 + (1, 1)0 + (1, 1)±11B = (1, 1)08l = (1, 3)0 + (1, 1)0 + (1, 2)±3/2All are interesting but the last-listed (1, 2)±3/2 are the bileptonic gauge bosons whichcan show up in Moller scattering.( e.g. e−e− −→ µ−µ−).Clearly such bileptons are a general featureof the embeddingSU(2)L ⊂ SU(3)and have the electric charges(Y −−, Y −) (L = +2)with antiparticles(Y ++, Y +) (L = -2).This feature of SU(15) grand unification re-emerges in the 3− 3− 1 model3 to whichwe now turn.3 − 3 − 1 is more economic, and anomaly cancellation is more elegant, compared toSU(15).To introduce the 3-3-1 model, the following are motivating factors:1. Consistency of a gauge theory requires cancellation of all chiral anomalies. Suchcancellation occurs for a quark-fermion family and is enough (almost) to fix allcharges.2. This does not explain Nf > 1 but is sufficiently impressive to suggest that Nf = 3may be explicable by anomaly cancellation in an extension. This requires extendedfamilies have non-zero anomaly and not all three families treated similarly.3. The third family is exceptional because of the top quark mass, and suggests+1 +1 -2 cancellation.4. There is such a -2 in the SM as the ratio of quark charges.5. Extension of SU(2)L to SU(3)L will have the same lepton couplings of the bileptonsas in SU(15).For the 3-3-1 model the gauge group is:SU(3)C × SU(3)L × U(1)XThe first family quarks are assigned toudDLūL d̄L D̄LThe triplet is a 3 of SU(3)L.The second family of quarks is assigned similarly:csSLc̄L s̄L S̄LThe third family of quarks is assigned differently:TtbLT̄L t̄L b̄LThe triplet in this case is a 3* of SU(3)L.The X quantum numbers of the triplets are equal to the electric charges of the centalmembers. That is, for the three families of quarks, X = −13, − 13, + 23.The leptons are assigned to 3*’s as follows:e+νee−Lµ+νµµ−Lτ+νττ−LThese three antitriplets have X = 0.Let us see how anomalies cancel. Recall that anomaly cancellation is crucial in manysituations of model-building beyond the standard model e.g. chiral color4 and instring theory5.The color anomaly (3L)3 cancels because QCD is vectorlike.The anomaly (3L)3 is non-trivial. Taking NC colors and Nl light neutrinos theanomaly cancels only if NC = Nl = 3.The remaining anomalies(3C)2X, (3L)2X, X3, X(Tµν)2also all cancel.In particular, each family has a non-zero anomaly for X3, (3L)2X and (3L)3; in eachcase the anomalies cancel proportionately to +1 +1 −2, as anticipated in the earlierdiscussion.To break the symmetry requires several Higgs multiplets.First an X = +1 triplet Φ with VEV < Φ >= (0, 0, U) breaks 331 to 321 and givesmasses to the D, S and T quarks as well as the gauge bosons Z ′ and Y . The scale Usets the scale for the new physics.Electroweak symmetry breaking requires two further triplets φ and φ′ with X = 0and X = −1 respectively. Their VEVs give mass to d, s, t and to u, c, b respectively.The first VEV also gives a family-antisymmetric contribution to the charged leptons.To obtain a general mass matrix for charged leptons necessitates adding a sextet withX = 0.THE NEW PHYSICS SCALE UThere is a lower bound from precision electroweak data:Z − Z ′ mixing dictates M(Z ′) > 300GeV .FCNC limits give a similar bound. For FCNC it is crucial that the third family bethe one treated asymmetrically. Otherwise the FCNC disagree with experiment.UPPER BOUND ON U:A bound on U arises because the embedding of 321 in 331 requires3 sin2θ < 1/4because for sin2θ = 1/4 the coupling gX diverges. This fixes U < 3TeV usingsin2θ(MZ) = 0.231. Hence M(Y ) cannot be higher than 1.5 TeV.LEP data:The highest precision high-energy data is from LEP. It gives6 M(Y ) > 120GeV .The best lower bounds come from low energy experiments:(1) Polarized muon decay7:M(Y ±) > 230 GeV.(2) Muonium-Antimuonium conversion8:M(Y ±±) > 850GeV .Just to recapitulate some of the points made at the beginning:e−e− collisions have never been studied above c.o.m. energy 1.12 GeV. An NLCshould have e−e− capability.Accomplishment of e−e− Collisions at NLC.In the post-SSC era it is desirable to avoid a third comma in the cost C, i.e.C < $1B.How can this be achieved?The cost of an NLC is roughly linear in the energy.A 500GeV NLC was costed last year at $7.9B, although I have been told informally9that that cost might be lowered below $5B. Thus 100GeV could be below $1B?Therefore the first fundable step could focus on luminosity rather than energy andbe a 100GeV machine with luminosity ∼ 1033. This is sufficiently above LEP to givea Giga-Z and allows an opportunity to do new machine physics.AcknowledgementsIt is a pleasure to thank Clemens Heusch for organizing a pleasant meeting andthe US Department of Energy for support under Grant No. DE-FG01-97ER41036.References1. W.C. Barber, G.K. O’Neill. B.J. Gittelman and B. Richter, Phys. Rev. D3,2796 (1971).2. P. H. Frampton and B. H. Lee, Phys. Rev. Lett. 64, 619 (1990).3. P. H. Frampton, Phys. Rev. Lett. 69, 2889 (1992);4. P.H. Frampton and S.L. Glashow, Phys. Lett. B190, 157 (1987); Phys. Rev.Lett. 58, 2168 (1987).5. P.H. Frampton and T.W. Kephart, Phys. Rev. Lett. 50, 1343 (1983); ibid 50,1347 (1983).6. P.H. Frampton and D. Ng, Phys. Rev. D45, 4240 (1992).7. A. Jodidio et al. Phys. Rev. D34, 1967 (1986); Err. D37, 237 (1988).8. L. Willmann et al. Phys. Rev. Lett. 82, 49 (1999).9. B. Richter, private communication (2000).Note AddedIn a recent work [P.H. Frampton and A. Rasin, UNC Report IFP-781-UNC (Febru-ary 2000)] we have updated the cross-section estimates for e−e− → µ−µ− in 6 whichused the SU(15) model. In the simpler 331-model the cross-section is about one orderof magnitude higher than the results in 6.

BILEPTON RESONANCE IN ELECTRON–ELECTRON SCATTERING

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Bilepton Resonance in Electron-Electron Scattering

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